Obama was originally scheduled for a four-nation, week-long trip to Asia, to advance his foreign policy goals and to meet with the leaders of the Asia-Pacific Economic Cooperation (APEC) nations in the Indonesian island Bali to negotiate a major trade deal.

Earlier this week, he canceled plans to visit the Philippines and Malaysia, fueling speculation that he may rule out the trip to Asia altogether.

The U.S. Congress has been unable to agree on the terms for the federal budget, plunging the government into a partial shutdown when the deadline for a deal expired at midnight on October 1.

In an exclusive interview with CNBC's John Harwood, President Obama admits that while he tries to remain calm, he is upset about his fight with House Republicans because "this is entirely unnecessary."

In an interview with CNBC on Wednesday , Obama said Wall Street needs to be genuinely worried about what is going on in Washington.

While gridlock in D.C. is nothing new, "this time I think Wall Street should be concerned," Obama said.

Analysts say the decision to cancel the trip to Asia could affect Obama's standing among his peers in the region.

"U.S. allies and partners in the region will worry that the United States is incapable of sustaining high-level engagement due to political paralysis at home," said Ernest Z. Bower, from the Center for Strategic & International Studies (CSIS), adding that the U.S. president risks undermining the "strategic trust that was hard-earned during the president's first term."